Question

what is the value of x in the figure?

Explanation:

Step1: Use the property of congruent triangles

Since \(AB = CD = 4.5\), \(AC = BD = 5.6\), and \(BC\) is common, \(\triangle ABC\cong\triangle DCB\) (by SSS - Side - Side - Side congruence criterion). So, \(\angle A=\angle D\), and the triangles \(\triangle ABC\) and \(\triangle DCB\) have the same angle measures.

Step2: Use the angle - sum property of a triangle

In \(\triangle ABC\), the sum of angles in a triangle is \(180^{\circ}\). Let's consider the right - hand triangle \(\triangle BCD\) (congruent to \(\triangle ABC\)). We know that in a triangle, the sum of interior angles is \(180^{\circ}\). For the triangle with angles \(53^{\circ}\), \(88^{\circ}\), and \(x^{\circ}\), we use the formula \(\angle1+\angle2+\angle3 = 180^{\circ}\).

$$53 + 88+x=180$$

$$141+x = 180$$

$$x=180 - 141$$

Answer:

\(39\)